3=-16t^2+256t+1680

Solution for 3=-16t^2+256t+1680 equation:

3=-16t^2+256t+1680

We move all terms to the left:

3-(-16t^2+256t+1680)=0

We get rid of parentheses

16t^2-256t-1680+3=0

We add all the numbers together, and all the variables

16t^2-256t-1677=0

a = 16; b = -256; c = -1677;
Δ = b2-4ac
Δ = -2562-4·16·(-1677)
Δ = 172864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{172864}=\sqrt{64*2701}=\sqrt{64}*\sqrt{2701}=8\sqrt{2701}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-256)-8\sqrt{2701}}{2*16}=\frac{256-8\sqrt{2701}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-256)+8\sqrt{2701}}{2*16}=\frac{256+8\sqrt{2701}}{32}
$